Related papers: Soft Constraints of Difference and Equality
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Many combinatorial problems deal with preferences and violations, the goal of which is to find solutions with the minimum cost. Weighted constraint satisfaction is a framework for modeling such problems, which consists of a set of cost…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…
Generally, multi-objective optimisation problems are solved exactly or approximated by solving a series of scalarisations, for example by dichotomic search. In this paper, we take a different approach and attempt to compute the set of all…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute.…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of…
We propose a new family of fairness definitions for classification problems that combine some of the best properties of both statistical and individual notions of fairness. We posit not only a distribution over individuals, but also a…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
To study the question under which circumstances small solutions can be found faster than by exhaustive search (and by how much), we study the fine-grained complexity of Boolean constraint satisfaction with size constraint exactly $k$. More…
Sequential Social Dilemmas (SSDs) provide a key framework for studying how cooperation emerges when individual incentives conflict with collective welfare. In Multi-Agent Reinforcement Learning, these problems are often addressed by…
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…
In a context where a decision has to be taken collectively by several agents, the social choice problem consists in deciding whether there exists a socially acceptable rule that aggregates the individual preferences of the agents into a…
We show that global constraints on finite domains like all-different can be reformulated into answer set programs on which we achieve arc, bound or range consistency. These reformulations offer a number of other advantages beyond providing…